Conventional dies of light emitting diodes of compound semiconductors (such as GaP, GaAsP, AlGaAs, et al in the III-V material group or ZnSe in the II-VI material group) usually emit light from the top surface. This top surface is parallel to the p-n junction plane of the dies. These dies are made by slicing into individual pieces a large processed epi wafer having electrodes already prepared on its top and bottom surfaces. More often than not, the wafer is sliced into columns of quadrilateral shape (normally as a square), when viewed along the norm of the p-n junction plane. Although these dies may be easy to obtain in terms of slicing throughput, the square-shaped product does not necessarily represent an optimal configuration in terms of other criteria.